Langevin diffusion of heavy quarks in non-conformal holographic backgrounds

TL;DR

This paper investigates the Langevin diffusion of heavy quarks in non-conformal holographic backgrounds, deriving analytic expressions for diffusion and friction coefficients, and comparing results with experimental data from RHIC.

Contribution

It provides a detailed holographic analysis of heavy quark diffusion in non-conformal backgrounds, including new analytic formulas and phenomenological comparisons.

Findings

Analytic expressions for Langevin coefficients in non-conformal backgrounds.

Modified Einstein relations between diffusion and friction.

Numerical estimates of jet-quenching parameter aligned with RHIC data.

Abstract

The Langevin diffusion process of a relativistic heavy quark in a non-conformal holographic setup is discussed. The bulk geometry is a general, five-dimensional asymptotically AdS black hole. The heavy quark is described by a trailing string attached to a flavor brane, moving at constant velocity. From the equations describing linearized fluctuations of the string world-sheet, the correlation functions defining a generalized Langevin process are constructed via the AdS/CFT prescription. In the local limit, analytic expressions for the Langevin diffusion and friction coefficients are obtained in terms of the bulk string metric. Modified Einstein relations between these quantities are also derived. The spectral densities associated to the Langevin correlators are analyzed, and simple analytic expressions are obtained in the small and large frequency limits. Finally, a numerical analysis of the jet-quenching parameter, and a comparison to RHIC phenomenology are performed in the case of Improved Holographic QCD.